S. Huang, Y. Ye, X. Han, W. Zuo, X. Zhang, L. Jiang 2019. “Performance evaluation of 1

heating tower heat pump systems over the world.” Energy Conversion and Management, 2

186, pp. 500-515. DOI: 10.1016/j.enconman.2019.03.003 3

Performance evaluation of heating tower heat pump systems 4

over the world 5

Shifang Huanga, b, Yunyang Yeb, Xu Hanb, Wangda Zuob, Xiaosong Zhanga, *, Li Jiangc 6

a School of Energy and Environment, Southeast University, Nanjing, 210096, PR China 7

b Department of Civil, Environmental and Architectural Engineering, University of Colorado Boulder, Boulder, CO 80309, U.S.A. 8

c Nanjing TICA Climate Solutions Co., Ltd, Nanjing, 210046, PR China 9

* Corresponding author. E-mail address: rachpe@seu.edu.cn (Xiaosong Zhang) 10

Abstract: Heating tower heat pumps (HTHPs) are proposed as an alternative to the conventional heat pumps. However, lacking 11

performance evaluation of the HTHPs in different regions limits their applications worldwide. To address this issue, this paper carries 12

out a large-scale comprehensive performance evaluation of the HTHPs in 869 typical locations. These locations are in the warm, mixed, 13

and cool climate zones, where buildings need both cooling and heating supply. Seven performance indices are adopted, including the 14

annual coefficient of performance (COP), COP in cooling season, COP in heating season, regeneration ratio, number of unsatisfactory 15

hours, matching degree of heat pump, and matching degree of heating tower. The performance evaluation of the HTHPs is conducted 16

by the processes of location selection, building load calculation, system sizing, simulation, and evaluation. The results show that the 17

HTHPs have excellent performance in the warm and mixed climate zones, where the average annual COPs are 4.67 and 3.68, 18

respectively. The HTHPs are also applicable in the cool climate zone with an average annual COP of 3.11. The distributions of all the 19

performance indices are presented through color maps, and the results are analyzed considering the air temperature and relative 20

humidity data of the locations. 21

Key words: heating tower heat pump; performance evaluation; locations; application; worldwide; coefficient of performance 22

1. Introduction 23

Chillers and boilers, air-source heat pumps (ASHPs), and ground-source heat pumps (GSHPs) are widely used 24

in the regions where buildings need both cooling and heating supply. Chillers have excellent performance in summer, 25

but they lie idle in winter and boilers are required to satisfy the heating load. However, the boilers can do harm to 26

the environment. The ASHPs, which can provide both cooling and heating, are becoming the most popular approach 27

because they can be conveniently installed and maintained. But low efficiency in summer and frosting issue in 28

winter significantly reduce its annual performance[1]. Su et al.[2] and Wang et al.[3] proposed a novel frost free ASHP, 29

which adopted liquid desiccant to reduce the humidity ratio of the air flowing through the heat exchangers. However, 30

this method can increase energy consumption and investment, and the issue of low efficiency in summer remains 31

unsolved. The GSHPs have high performance in both summer and winter, however, they are subject to topographical 32

conditions and relatively high initial cost[4]. To address these issues, heating tower heat pumps (HTHPs), as novel 33

integrated heating and cooling units, have been proposed as an alternative to the conventional heat pump systems. 1

The HTHPs have the advantages of high cooling efficiency similar to water chiller and cooling tower systems in 2

summer. In winter, the HTHPs replace the boilers by using ambient air as a low-potential heat source, which 3

improves facility utilization ratio and energy efficiency. In addition, the HTHPs address the frosting issue 4

substantially, and they are easy to install like the ASHPs without the limitation of topographical conditions[5]. 5

The previous studies focus more on the mechanism of the components of the HTHP systems, such as heating 6

towers and regeneration devices. Tan et al.[6] made a revision on the Merkel’s equation of standard cooling towers 7

to calculate the thermal characteristics of a heating tower, which is also named as reversibly used water cooling 8

tower in their study. Fujita et al.[7][8] developed a overall enthalpy transfer model for both counter and cross flow 9

heating towers, and figured out the overall enthalpy transfer coefficients by experiments. Lu et al.[9] developed a 10

coupled heat and mass transfer model for the heating tower. By combining this model and the experimental data, 11

Wen et al.[10] figured out the heat transfer coefficient of a open-type heating tower by assuming Lewis number equal 12

to one. Then, Huang et al.[11] carried out a more detailed experimental investigation and presented the influence of 13

the inlet air/solution parameters on the performance of the heating tower. In addition, the coupled heat and mass 14

transfer coefficients were calculated and correlation expressions were developed in this study. Song et al.[12] 15

conducted a similar study on a closed-type heating tower, and compared the results with the heat and mass transfer 16

process in the liquid desiccant field. Cui et al.[13][14] experimentally studied the performance of upward and 17

downward spraying heating towers, and found they had higher heating efficiency than the ones using gravity 18

distribution. As for the numerical studies on the performance of heating tower, both Wu et al.[15] and Zendehboudi 19

[16] proposed an artificial neural network model. The results in their studies are in good agreement with the 20

experimental data. Since the heating towers can absorb water vapor from the ambient air, the regeneration devices 21

are necessary to achieve mass balance. Liang et al.[17] and Huang at al.[18] found that the heating tower can achieve 22

self-regeneration in warm and dry working conditions. Huang at al.[5] further proposed that the main reason of the 23

self-regeneration lies in the energy storage characteristic of the solution, and a good amount of regeneration energy 24

can be saved by taking full advantage of the self-regeneration process. However, the self-regeneration is subjected 25

to the weather condition. To address this problem, Ai et al.[19] proposed a mechanical vapor recompression approach, 26

and Wen at al.[20] investigated a vacuum boiling and condensation approach. Both approaches were found to be more 27

efficient than the conventional evaporation regeneration approaches because they utilized the condensing heat of 28

water vapor. 29

The HTHPs have shown advantages over the conventional building cooling and heating systems in some pilot 30

studies in a few cities. However, their performances have not been systemically evaluated for potential applications 31

worldwide. Although several experimental studies are related to the system performance (summarized in Table 1), 32

there are limitations for the evaluations: (1) each study was carried in a specific location in China; (2) there were 33

huge differences in components and capacities in different studies; (3) the experiments were conducted under only 34

one weather condition or small ranges of temperature and relative humidity; (4) only coefficient of performance in 1

heating season, 𝐶𝑂𝑃ℎ, was adopted for evaluation. A large-scale comprehensive performance evaluation of HTHPs 2

would help identify their application potential in more regions. However, when conducting such large-scale 3

evaluation, the research should meet the following requirements: (1) the locations should be selected over the world; 4

(2) the HTHP systems should be designed and sized under the same standard; (3) the HTHP systems should be 5

running for a calendar year, which includes both cooling and heating seasons, and consider the part load ratio of the 6

systems; (4) the indices should be able to present the performance comprehensively, including the 𝐶𝑂𝑃 in cooling 7

season, 𝐶𝑂𝑃 in heating season, mean 𝐶𝑂𝑃 in one year, and regeneration ratio. 8

Table 1. Summary of studies on system performance of HTHPs 9

Literature Location Tower type Solution Compressor Heating

capacity Outdoor weather COPh

Liang et al.[21] Nanjing Open-type Glycol Rotor 5 kW Ta=-2℃ [2.72, 3.02]

Wu et al.[22] Changsha Open-type CaCl2 Screw 125 kW Ta=4.6℃, φa=90% [2.70, 2.86]

Zhang et al.[23] Nanjing Open-type Glycol Rotor 7 kW Ta=6.5℃, φa=76% 3.02

Li et al.[24] Changsha Closed-type Urea Screw 125 kW Ta=[-1, 5]℃,

φa=[71%, 95%] [2.58, 3.90]

Cheng et al.[25] Changsha Closed-type / Scroll 809 kW Ta=4.3℃, φa=93.9% 3.00

Chen et al.[26] Hangzhou Open-type / Screw / Ta=[-3, 4] ℃ [3.00,3.73]

To address the above problems, this paper carries out a large-scale comprehensive performance evaluation of 10

the HTHPs over the world. Firstly, the HTHP model is developed and validated. Then, the performance evaluation 11

of the HTHPs is implemented by the processes of location selection, building load calculation, system sizing, 12

simulation, and evaluation. Seven performance indices are proposed and adopted to carry out a comprehensive 13

evaluation. Finally, all the results are presented through color maps, and the distributions are analyzed by using air 14

temperature and relative humidity data of the locations. 15

2. System description and modeling 16

2.1. Description of HTHP system 17

Fig. 1 demonstrates the schematics of a typical HTHP system, including a heating tower, a heat pump, a 18

regeneration device, a solution tank, four pumps, and eight valves. In the cooling season, the HTHP system works 19

as a chiller with a cooling tower, with valves 1-4 open and valves 5-8 closed. The evaporator of the heat pump is 20

connected with user sides supplying chilled water to the buildings. The condenser of the heat pump is coupled with 21

the heating tower, in which water is adopted and evaporates in the tower to reject heat to the ambient air. Make-up 22

water is added to this loop to achieve mass balance. The regeneration loop, including the regeneration device, 23

solution tank, and solution pumps, is shut down in the cooling season. 24

In the heating mode, valves 5-8 are open, while valves 1-4 are closed. The condenser of the heat pump supplies 1

hot water to the building. The evaporator is connected to the heating tower for absorbing heat from the ambient air. 2

In this loop, solution with low freezing point (e.g. glycol aqueous, calcium chloride aqueous) is adopted instead of 3

water to avoid system freeze. In some conditions, the solution may absorb both heat and mass from the ambient air. 4

As a result, the solution becomes diluted, which increases risks of system freeze. To address this problem, a 5

regeneration device based on vacuum boiling and condensation is employed to achieve mass balance[20]. The 6

solution tank is equipped to store dilute solution temporarily in the heating season to make full use of the self-7

regeneration process. Also, it is used for solution storage in the cooling and transition seasons. 8

Fig. 1. The schematic of the HTHP system

2.2. Modeling of HTHP system 9

The models for all the components of the studied HTHP system are developed separately, and then coupled by 10

balancing heat, mass and energy between different components. The following sections describe the models for the 11

heat pump, heating tower, and regeneration device, respectively. 12

2.2.1. Heat pump model 13

The heat pump consists of four main components, including the screw compressor, shell-tube evaporator, shell-14

tube condenser, and thermostatic expansion valve. Models of the components are developed as follows. 15

Compressor 16

The refrigerant mass flow rate, 𝑀𝑅, and power consumption, 𝑊𝑐𝑜𝑚𝑝, for screw compressors can be expressed 17

by a function of the evaporating temperature, 𝑇𝑒 , and condensing temperature, 𝑇𝑐 [27], and rotation speed 18

𝑁𝑐𝑜𝑚𝑝[28][29]: 19

𝑀𝑅 = (α1 + α2𝑇𝑒 + α3𝑇𝑐 + α4𝑇𝑒2 + α5𝑇𝑒𝑇𝑐 + α6𝑇𝑐

2 + α7𝑇𝑒3 + α8𝑇𝑒

2𝑇𝑐 + α9𝑇𝑒𝑇𝑐2 + α10𝑇𝑐

3)𝑁𝑐𝑜𝑚𝑝

𝑁𝑐𝑜𝑚𝑝,𝑟𝑎𝑡𝑒𝑑, (1)

𝑊𝑐𝑜𝑚𝑝 = (𝛽1 + 𝛽2𝑇𝑒 + 𝛽3𝑇𝑐 + 𝛽4𝑇𝑒2 + 𝛽5𝑇𝑒𝑇𝑐 + 𝛽6𝑇𝑐

2 + 𝛽7𝑇𝑒3 + 𝛽8𝑇𝑒

2𝑇𝑐 + 𝛽9𝑇𝑒𝑇𝑐2 +

𝛽10𝑇𝑐3)

𝑁𝑐𝑜𝑚𝑝

𝑁𝑐𝑜𝑚𝑝,𝑟𝑎𝑡𝑒𝑑,

(2)

where the subscript 𝑟𝑎𝑡𝑒𝑑 represents the performance under rated speed. The 𝛼1−10 and 𝛽1−10 are coefficients 1

regressed from experimental data provided by manufacturer BITZER. 2

Evaporator and condenser 3

The classical logarithmic mean temperature difference method is adopted in both evaporator and condenser 4

models. The cooling capacity of the evaporator, 𝑄𝑒, and the heating capacity of the condenser, 𝑄𝑐, can be expressed 5

as follows: 6

𝑄𝑒 = 𝐾𝑒𝐴𝑒𝐿𝑀𝑇𝐷𝑒 , (3)

𝑄𝑐 = 𝐾𝑐𝐴𝑐𝐿𝑀𝑇𝐷𝑐 , (4)

where 𝐾 , 𝐴 , and 𝐿𝑀𝑇𝐷 are the heat transfer coefficient, heat transfer area, and logarithmic mean temperature 7

difference between refrigerant and water/ solution. The subscript 𝑒 represents the evaporator, and 𝑐 represents the 8

condenser. 9

The overall heat transfer coefficient for the evaporator or condenser, 𝐾𝑒 (𝐾𝑐), can be expressed as a function 10

of the heat transfer coefficient inside the tube, 𝐾𝑖, and outside the tube, 𝐾𝑜: 11

𝐾𝑒 (𝐾𝑐) =1

(1

𝐾𝑖+𝑅𝑖)

𝐴𝑜𝐴𝑖

+𝛿𝐴𝑜

𝜆𝑤𝑎𝑙𝑙𝐴𝑚+𝑅𝑜+

1

𝐾𝑜

, (5)

where 𝑅 is the heat transfer resistance. The 𝛿 is the thickness of the wall. The subscripts 𝑖 and 𝑜 represent the 12

property inside and outside the tube, respectively. And the subscripts 𝑚 is the mean value of the inside and outside 13

property. The heat transfer coefficients for the evaporation of R22 inside the tube, condensation of R22 outside the 14

tube, and water/solution across the tube can be found in our pervious studies[5]. 15

The heat transfer capacities of the evaporator and condenser can be expressed by the energy variations of 16

refrigerant and water/solution. 17

𝑄𝑒 = 𝑀𝑅(ℎ1 − ℎ4) , (6)

𝑄𝑒 = 𝐶𝑝𝑤𝑀𝑐ℎ𝑤(𝑇𝑐ℎ𝑤𝑟 − 𝑇𝑐ℎ𝑤𝑠) or 𝑄𝑒 = 𝐶𝑝𝑠𝑀𝑠(𝑇𝑠𝑠 − 𝑇𝑠𝑟) , (7)

𝑄𝑐 = 𝑀𝑅(ℎ2 − ℎ3) , (8)

𝑄𝑐 = 𝐶𝑝𝑤𝑀𝑐𝑤(𝑇𝑐𝑤𝑟 − 𝑇𝑐𝑤𝑠) 𝑜𝑟 𝑄𝑐 = 𝐶𝑝𝑤𝑀ℎ𝑤(𝑇ℎ𝑤𝑠 − 𝑇ℎ𝑤𝑟) , (9)

where ℎ1 and ℎ4 are the enthalpy of the refrigerant in the outlet and inlet of the evaporator, ℎ2 and ℎ3 are the 18

enthalpy of the refrigerant in the inlet and outlet of the condenser. 19

Expansion valve 20

The expansion process in the expansion valve is taken as an isenthalpic process as shown in Eq.(10). The mass 21

flow rate of the refrigerant can be calculated[30]: 22

ℎ3 = ℎ4 , (10)

𝑀𝑅 = 𝐶𝐷𝐴𝑡ℎ√𝜌𝑅,𝑙 (𝑃𝑐 − 𝑃𝑒) , (11)

where, 𝐶𝐷 is the constant mass flow coefficient. The 𝐴𝑡ℎ represents the geometric throat area of the thermostatic 1

expansion valve, which is adjustable and controlled by the superheat. The 𝑃𝑐 and 𝑃𝑒 are the pressure of condenser 2

and evaporator, respectively. 3

2.2.2. Heating tower model 4

The heating tower model in winter is developed using a finite difference method[11][18]. Eqs.(12) and (13) 5

express the energy and mass balances between air and solution. Eq.(14) describes the solute balance of the solution. 6

𝑚𝑎𝑑ℎ𝑎 = −𝐶𝑝𝑠𝑚𝑠𝑑𝑇𝑠 − 𝐶𝑝𝑠𝑇𝑠𝑑𝑚𝑠 , (12)

𝑑𝑚𝑠 = −𝑚𝑎𝑑𝜔𝑎 , (13)

𝑋𝑠𝑚𝑠 = (𝑋𝑠 + 𝑑𝑋𝑠)(𝑚𝑠 + 𝑑𝑚𝑠) , (14)

where 𝑑ℎ𝑎 is the enthalpy variation of the air through an element. The 𝑑𝑇𝑠, 𝑑𝑚𝑠 and 𝑑𝑋𝑠 represent the variations 7

of the solution in temperature, mass flow rate and concentration through an element, respectively. The 𝑋𝑠 is the 8

mass concentration of the solution. 9

The convective heat and mass transfer are also applied as follows: 10

ℎ𝑐𝐿 ∙ 𝑑𝑥 ∙ 𝑑𝑦 ∙ 𝛼𝑤(𝑇𝑠 − 𝑇𝑎) = 𝑚𝑎(𝐶𝑝𝑎 + 𝜔𝑎𝐶𝑝𝑣)𝑑𝑇𝑎 , (15)

ℎ𝑑𝐿 ∙ 𝑑𝑥 ∙ 𝑑𝑦 ∙ 𝛼𝑤(𝜔𝑠 − 𝜔𝑎) = 𝑚𝑎𝑑𝜔𝑎 , (16)

where 𝜔𝑠 is the equivalent humidity ratio of the solution, 𝑑𝑇𝑎 and 𝑑𝜔𝑎 are the temperature and humidity ratio 11

variation of air through an element. The 𝑑𝑥 ∙ 𝑑𝑦 represents the size of each element, 𝐿 is the length of the packing, 12

and 𝛼𝑤 is the specific area of the packing. The ℎ𝑐 is the heat transfer coefficient, ℎ𝑑 is the mass transfer 13

coefficient. These two coefficients are expressed as functions of the solution mass flow flux, 𝐺𝑠, and air mass flow 14

flux, 𝐺𝑎: 15

ℎ𝑐 = 𝛾1𝐺𝑠𝛾2𝐺𝑎

𝛾3 , (17)

ℎ𝑑 = 𝜉1𝐺𝑠𝜉2𝐺𝑎

𝜉3 , (18)

The coefficients 𝛾1−3 and 𝜉1−3 are regressed from experimental data of our previous study[11]. 16

By replacing the subscript 𝑠 by 𝑤 and setting 𝑋𝑠 to zero, the model listed above can also be used to simulate 17

the performance of heating tower in cooling season. The heat and mass transfer capacities in both cooling and 18

heating seasons can be expressed as follows: 19

𝑄𝑠ℎ = (𝐶𝑝𝑎 + 𝜔𝑎𝐶𝑝𝑣) ∙ 𝑀𝑎 ∙ (𝑇𝑎,𝑜 − 𝑇𝑎,𝑖) , (19)

𝑄𝑙ℎ = 𝑟𝑣 ∙ 𝑀𝑎 ∙ (𝜔𝑎,𝑜 − 𝜔𝑎,𝑖) , (20)

where 𝑄𝑠ℎ is the sensible heat transfer capacity, and 𝑄𝑙ℎ is the latent heat transfer capacity. Here, the positive 20

values of 𝑄𝑠ℎ and 𝑄𝑙ℎ mean that the heat and mass transfer directions are from air to condenser water or solution. 21

When the values are negative, the directions are the opposite. The 𝐶𝑝, 𝑀, 𝑇, 𝜔, and 𝑟 represent the specific heat, 22

mass flow rate, temperature, humidity ratio, and vaporization latent heat, respectively. The subscripts 𝑎, 𝑣, 𝑖, and 23

𝑜 represent the air, water vapor, tower inlet, and tower outlet, respectively. 24

2.2.3. Regeneration model 1

A regeneration module based on vacuum boiling and condensation is adopted in this study to satisfy the 2

regeneration demand in winter. The adopted module approximates the efficiency of the regeneration system, 𝜂𝑅𝐷, 3

as a constant of 3.4 kg/kWh[20]. This is because the performance of this regeneration method is independent of the 4

weather conditions. Then the power input for the regeneration, 𝑊𝑅𝐷, can be calculated by the following equation: 5

𝑊𝑅𝐷 =∫

𝑄𝑙ℎ𝑟𝑤

𝑑𝑡

𝜂𝑅𝐷 . (21)

2.3. Validation of models 6

The physics-based model developed in this study is validated using our experimental data[5], as shown in Fig. 7

2. The relative error is within ±10% for all the predicted values, and the average error is 3.48% for cooling/heating 8

capacity, and 3.05% for the COP. This indicates that the physics-based model has high accuracy in predicting the 9

performance of the HTHP. However, in most experimental runs, the predicted cooling/heating capacity is a little bit 10

higher than the experimental capacity. There are two reasons: 1) In our models, the heat exchangers and pipelines 11

are well adiabatic, while the real system can not reach 100% adiabatic condition. Therefore, there is some heat 12

leakage from the hot water to the surroundings in the winter condition, and some heat absorption from the 13

surroundings to the chilled water in the summer condition. 2) The real system has dirt in the heat exchangers, which 14

can weaken the heat transfer process. Therefor, the experimental cooling/heating capacity can be less than the 15

predicted capacity. 16

(a) Cooling/heating capacity (b) COP

Fig. 2. Comparison between the experimental data and the model prediction of the HTHP

3. Performance evaluation of HTHP systems 17

The performance evaluation of HTHPs over the world is carried out by the steps of location selection, building 18

load calculation, system sizing, simulation, and evaluation, as shown in Fig. 3. The location selection step is to 19

determine the potential thermal climate zones (locations) for HTHPs’ application. The building load calculation and 20

system sizing steps are conducted to provide input parameters for system simulations in different locations. In the 1

simulation step, hourly simulation for each case is carried out by coupling weather, building, and HTHP system. In 2

the evaluation step, seven performance indices are proposed to realize a comprehensive evaluation. The details of 3

all the steps will be demonstrated in the following sections. 4

Building Model

EnergyPlus

Design Building Cooling

and Heating Load

Hourly Building Cooling

and Heating Load

Coupled Hourly Simulation: 8760 Hours

System Schedule

Locations

Pre-selection: Warm Zone, Mixed Zone, Cool Zone

Potential Locations

Design Tower Cooling and

Heating Capacity

Heat Pump Model Heating Tower Model

HaltCooling Mode Heating Mode

Assumption: N , te , tc , tss

Expansion: MR , h3 , te , tc → Ath , h4

| tsc - tsc’| ≤ ε5

Evaporator: MR , h4 , te , Ms , tss , Xss→ Qe , tsr

| Qc - Qe - Wcomp | ≤ ε7

Heating tower: Ma , ta,i , wa,i , Ms , tsr , Xsr → Qs , Ql , tss , Xss

| Qs + Ql - Qe | ≤ ε6

Yes

No

No

Yes

Compressor: N , te , tc , tsh , h1 → MR , Wcomp , h2

Condenser: MR , h2 , tc , Mhw , thws → Qc , h3 , tsc , thwr

Step 1: Pre-selection

Step 2: Building Load Calculation

Step 3: System Sizing

Yes

YesNo

| Qc- Qload | ≤ ε8

Start

Assumption: N , te , tc , tcws

Expansion: MR , h3 , te , tc → Ath , h4

| tsc - tsc’| ≤ ε1

Evaporator: MR , h4 , te , Mchw , tchws → Qe , tcwhr

| Qc - Qe - Wcomp | ≤ ε3

Heating tower: Ma , ta,i , wa,i , Mcw , tcwr→ Qs , Ql , tcws

| Qs + Ql - Qc | ≤ ε1

Yes

No

Compressor: N , te , tc , tsh , h1 → MR , Wcomp , h2

Condenser: MR , h2 , tc , Mcw , tcws → Qc , h3 , tsc , tcwr

Yes

| Qe - Qload | ≤ ε4

NoYes

No

No

Yes

tf - te ≥ ε9

No

Yes

Vsys - Vs ≥ ε10

No

No

Performance Indices: ηMDHP, ηMDHT, COPc, ηRR, NUH, COPh, COPa

End

Step 4: Simulation

Update: tcws

Update: tc

Update: te

Update: N

Update: tc

Update: tss

Update: te

Update: N

Regeneration:

Ql , Xss→ WRD , Xsr

Weather Data

Yes

Step 5: Evaluation

Fig. 3. Flow chart of the performance evaluation of HTHPs over the world

3.1. Selection of Locations 5

The location selection process is carried out first to exclude the regions which are clearly unsuited for the 6

application of the HTHPs. To determine the thermal climate zones for locations over the world, cooling degree-day 7

base 10°C (CDD10°C) and heating degree-day base 18°C (HDD18°C) are adopted, according to ANSI/ASHRAE 1

Standard 169-2013[31]: 2

CDD10°C = ∑ max ((1

24∑ 𝑇𝑎 − 10)24

ℎ𝑟=1365𝑑𝑎𝑦=1 , 0) , (22)

HDD18°C = ∑ max ((18.3 −1

24∑ 𝑇𝑎)24

ℎ𝑟=1365𝑑𝑎𝑦=1 , 0) . (23)

According to the ranges of the CDD10°C and HDD18°C, nine thermal climate zones are defined, including Zone 0 3

(extremely hot), Zone 1 (very hot), Zone 2 (hot), Zone 3 (warm), Zone 4 (mixed), Zone 5 (cool), Zone 6 (cold), 4

Zone 7 (very cold), and Zone 8 (subarctic/arctic), as shown in Fig. 4. The buildings in Zones 0-2 only require cooling 5

supply, which can be satisfied by chillers. Similarly, boils are suitable for the buildings in Zones 6-8, which only 6

require heating supply, and heat pumps have poor performance in such cold regions. Zones 3-5, where buildings 7

need both cooling and heating supply, are considered as the potential regions for the application of HTHPs. 8

Weather data for 2,581 locations is downloaded from EnergyPlus website (https://energyplus.net/weather). 9

Then, the CDD10°C and HDD18° for all the locations are calculated. After the selection process, 869 locations in 10

Zones 3-5 are left, as presented in Fig. 4. Most locations are in China (50, 34, 36 locations in Zones 3-5, respectively), 11

the USA (169, 155, 180 locations in Zones 3-5, respectively), and Europe (69, 50, 38 locations in Zones 3-5, 12

respectively). The other locations are in the rest of the world (65, 17, 6 locations in Zones 3-5, respectively), such 13

as Japan, Australia, and Argentina. The distribution of selected locations is demonstrated in Fig. 5. 14

Fig. 4. Thermal climate zones

15

Fig. 5. Distribution of selected locations over the world

3.2. Building load calculation 1

In the building load calculation process, reference office building models developed by U.S. Department of 2

Energy (DOE) are adopted. These reference building models are complete descriptions for whole building energy 3

analysis, and organized by climate zones (here, A represents the humid zone, B represents the dry zone, and C 4

represents the marine zone[31]). The reference buildings have the same shape and architecture, as shown in Fig. 6. 5

The details of the settings of envelop, occupancy, and equipment, are demonstrated in Table 2. 6

Fig. 6. Building shape and architecture

Table 2. Building characteristics in different climate zones 7

Building characteristics Climate zones

3A 3B 3C 4A 4B 4C 5A 5B

1 General information

Total floor area m2 4,982

Cooling indoor set point °C 24

Heating indoor set point °C 21

Indoor RH % 60

2 Building envelope

R-value of exterior wall m2 K W-1 1.36 1.10 1.36 1.98 1.76 1.92 2.15 2.15

R-value of roof m2 K W-1 2.44 3.66 2.00 3.03 2.99 2.75 3.38 3.51

U-value of windows W m-2 K-1 4.09 5.84 4.09 3.35 4.09 4.09 3.35 3.35

SHGC of windows / 0.26 0.25 0.39 0.36 0.36 0.39 0.39 0.39

Window-to-wall ratio / 0.33

3 Zone summary

Occupant density (m2 person-1) 18.58

Ventilation rate (l s-1 person-1) 10

Lighting load (W m-2) 16.90

Equipment load (W m-2) 10.76

Infiltration rate (ACH) Perimeter: 0.98-1.03; Mid-floor:0.41; Top-floor: 3.76

Based on the reference building models and settings mentioned above, we used Python to call EnergyPlus to 1

calculate the building loads for the 869 locations. Building loads are used as input data for the system sizing, 2

simulation, and evaluation, which will be presented in Sections 3.3 to 3.5. 3

3.3. Design and sizing of HTHP system 4

A series of heat pumps are designed to satisfy the different building loads of the 869 locations. In the nominal 5

cooling condition, the supply and return chilled water temperature are 7 and 12°C, and the supply and return cooling 6

water temperature are 30 and 35°C. In the nominal heating condition, the supply and return solution temperature 7

are -1 and 1.5°C, and the supply and return hot water temperature are 40 and 45°C. The cooling and heating 8

capacities, 𝐶𝑂𝑃𝑐, and 𝐶𝑂𝑃ℎ in the nominal cooling and heating conditions are presented in Table 3. 9

Table 3. Parameters of designed heat pumps in nominal conditions 10

Heat pump type Cooling capacity Heating capacity COPc COPh

kW kW / /

HEZEHP080CSH 81 73 4.22 3.39

HEZEHP100CSH 100 92 4.20 3.44

HEZEHP140CSH 135 121 4.28 3.37

HEZEHP160CSH 155 139 4.32 3.40

HEZEHP190CSH 187 171 4.29 3.44

HEZEHP200CSH 203 184 4.38 3.52

HEZEHP210CSH 215 197 4.34 3.46

HEZEHP250CSH 254 230 4.51 3.55

HEZEHP280CSH 281 256 4.43 3.52

HEZEHP320CSH 319 291 4.43 3.52

HEZEHP380CSH 380 343 4.48 3.53

HEZEHP440CSH 440 396 4.58 3.65

HEZEHP510CSH 505 461 4.59 3.66

HEZEHP570CSH 574 523 4.61 3.67

In addition, a series of heating towers are designed to satisfy the different heat rejection and absorption 1

capacities of the heat pumps. In the nominal cooling condition, the air dry/wet-bulb temperature is 32°C/28°C, the 2

air/water flow flux of the heating tower is 2 kg m-2 s-1/4 kg m-2 s-1, and the supply and return cooling water 3

temperature are 30 and 35°C. In the nominal heating condition, the air dry/wet-bulb temperature is 7°C/6°C, the 4

air/water flow flux of the heating tower is the same as that in cooling condition, the supply and return solution 5

temperature are -1 and 1.5°C. In this study, we adopt glycol aqueous as working fluid in heating condition, and its 6

concentration is 15% in the nominal condition. The parameters of the designed heating towers, including heat 7

rejection and absorption capacities, air and water (solution) mass flow rates, are demonstrated in Table 4. 8

Table 4. Parameters of designed heating towers in nominal conditions 9

Heating tower type Heat rejection capacity Heat absorption capacity Water/solution flow rate Air flow rate

kW kW m3 h-1 m3 h-1

HEZEHT130060 132 55 22 24,925

HEZEHT200080 198 82 33 37,388

HEZEHT260110 264 109 44 49,850

HEZEHT330140 330 136 55 62,313

HEZEHT400160 396 164 66 74,776

HEZEHT460190 462 191 77 87,238

HEZEHT530220 528 218 88 99,701

HEZEHT590250 594 246 99 112,164

HEZEHT660270 660 273 110 124,626

HEZEHT730300 726 300 121 137,089

HEZEHT790330 793 328 132 149,551

HEZEHT860360 859 355 143 162,014

HEZEHT930380 925 382 154 174,477

HEZEHT990410 991 409 165 186,939

After the design of the heat pumps and heating towers, the sizing of the HTHPs for different cases can be done 10

with the calculated building loads. Here, we give two examples to show the sizing process. For city Wuhan, China, 11

the designed building cooling/heating load is 411 kW/253 kW, and the corresponding tower heat 12

rejection/absorption load is 500 kW/184 kW. Therefore, heat pump HEZEHP440CSH (440 kW/396 kW) and 13

heating tower HEZEHT530220 (528 kW / 218 kW) are selected to satisfy both cooling and heating demand. For 14

city Beijing, China, the designed building cooling/heating load is 369 kW/297 kW, and the corresponding tower 15

heat rejection/absorption load is 451 kW/213 kW. So, heat pump HEZEHP380CSH (380 kW/343 kW) and heating 16

tower HEZEHT530220 (528 kW / 218 kW) are selected. 17

3.4. Simulation of HTHP system 18

The weather data, building loads, and system parameters of the selected 869 locations obtained by Steps 1-3 19

are inputs of Step 4 (simulation). For each location, the simulation of 8,760 hours in one calendar year is carried 20

out, as shown in Fig. 3. According to the building schedule, the modes of the HTHP is selected first, including 1

cooing, heating, and halt modes. Then, the models of the components mentioned in Section 2.2 are implemented in 2

the MATLAB environment. To solve the non-linear models which are linked by energy and mass balances, a newton 3

iterative method is applied. In the cooling mode, the rotation speed of the compressor, evaporating temperature, 4

condensing temperature, and cooling water supply temperature are selected as iteration variables. The newton 5

iteration is used to update the iteration variables according to the energy and mass balances between outdoor air, 6

cooling water, refrigerant, and chilled water. In this paper, the superheating and subcooling values are both set as 5°7

C. In the real system, we adjust the geometric throat area of the thermal expansion valve, 𝐴𝑡ℎ, to make sure that the 8

superheating value reaches its set point. But the 𝐴𝑡ℎ has a physical constraint, which can only be adjusted from 0% 9

to the 100% opening. So, we also calculate and record the 𝐴𝑡ℎ in the 'Expansion' module. In the most conditions, 10

the 𝐴𝑡ℎ is in the above range since we select appropriate thermostatic expansion valves for all the heat pumps listed 11

in our manuscript. In some extreme condition when the 𝐴𝑡ℎ exceeds the maximum value, we set the 𝐴𝑡ℎ as the 12

maximum value, and then set the superheating value as an unknown. In the heating mode, the cooling water is 13

replaced by glycol aqueous as the working fluid in the heating tower, and chilled water is replaced by hot water. In 14

addition, the regeneration device is coupled with the evaporator and heating tower. As mentioned in Section 2.1, the 15

heating tower absorbs both heat and mass (water) from the ambient air in some conditions. Fortunately, the heating 16

tower is also able to evaporate the excessive water when the water vapor pressure of the solution is higher than that 17

of the air[18]. This process named as “self-regeneration” can reduce the regeneration load and energy consumption[5]. 18

In order to make full use of the self-regeneration process, the regeneration device only runs when the freezing point 19

of the solution is not low enough or the volume of the solution is larger than the storage capacity of the system. The 20

solution with higher concentration has lower freezing point, which can prevent system from freeze and improve the 21

system safety. However, the increase of concentration can also reduce the water vapor pressure of the solution, 22

which means that the solution will absorb more latent heat from the ambient air. As a result, the energy consumption 23

of the regeneration device will increase significantly. So, the ideal state is keeping the safety margin close to 0 °C, 24

which is the difference between the solution temperature in the outlet of the evaporator and the freezing point of the 25

solution. In this study, by considering the measuring error and system response time in the real project, we set the 26

safety margin as 3 °C. 27

3.5. Evaluation of HTHP system 28

As indicated in the introduction, only 𝐶𝑂𝑃ℎ was adopted for evaluation of HTHP’ operational performance 29

in heating season in the previous studies. However, more performance indices are required in the designing and 30

evaluating process of a building’s cooling and heating system. For instance, there are three alternatives for a real 31

project: chiller and boiler, ASHP, and HTHP. Commonly, we need to compare the initial cost and annual energy 32

consumption to carry out the economic analysis. Besides the 𝐶𝑂𝑃ℎ, we still need to know the coefficient of 33

performance of the HTHP in cooling season, the required capacity and energy consumption of the regeneration 34

device. Besides the new newly established system, the HTHP system can also be used to transformation a 1

conventional water-cooled chiller system to satisfy both cooling and heating demands. In this case, we need to know 2

if additional towers or heat pump hosts are required, which can have an influence on the initial cost. Therefore, we 3

propose the matching degree of heat pump and the matching degree of heating tower to address the above problem. 4

The detailed definitions and functions of these performance indices are listed as follows. 5

The matching degree of heat pump in cooling and heating modes, 𝜂𝑀𝐷𝐻𝑃, is defined as: 6

𝜂𝑀𝐷𝐻𝑃 =𝑄𝐷𝐵𝐶/𝑄𝐷𝐵𝐻

𝑄𝐻𝑃𝐶/𝑄𝐻𝑃𝐻 , (24)

where 𝑄𝐷𝐵𝐶 and 𝑄𝐷𝐵𝐻 mean the designed building cooling and heating loads, respectively. The 𝑄𝐻𝑃𝐶 and 𝑄𝐻𝑃𝐻 7

are the heat pump cooling and heating capacities, respectively. When 𝜂𝑀𝐷𝐻𝑃 is larger than 1, it indicates that the 8

heat pump should be sized according to the cooling mode in new HTHP system, or no additional heat pumps is 9

required in the transformation of a chiller system into a HTHP system. When 𝜂𝑀𝐷𝐻𝑃 is less than 1, the conclusions 10

are the opposite. 11

The matching degree of heating tower in cooling and heating modes, 𝜂𝑀𝐷𝐻𝑇, is defined as: 12

𝜂𝑀𝐷𝐻𝑇 =(𝑄𝐷𝐵𝐶+

𝑄𝐷𝐵𝐶𝐶𝑂𝑃𝑐,𝑟𝑎𝑡𝑒𝑑

)/(𝑄𝐷𝐵𝐻−𝑄𝐷𝐵𝐻

𝐶𝑂𝑃ℎ,𝑟𝑎𝑡𝑒𝑑)

𝑄𝐻𝑇𝐶/𝑄𝐻𝑇𝐻 , (25)

where 𝐶𝑂𝑃𝑐,𝑟𝑎𝑡𝑒𝑑 and 𝐶𝑂𝑃ℎ,𝑟𝑎𝑡𝑒𝑑 are the rated cooling and heating coefficients of the heat pump, respectively. 13

The 𝑄𝐻𝑇𝐶 and 𝑄𝐻𝑇𝐻 are the heating tower cooling and heating capacities, respectively. Similarly, the heating 14

tower should be sized to satisfy the tower cooling load in new system, or no additional heating tower is required in 15

transformation, when 𝜂𝑀𝐷𝐻𝑇 is greater than 1. 16

The regeneration ratio in the winter conditions, 𝜂𝑅𝑅, is define as follow: 17

𝜂𝑅𝑅 =∫ 𝑄𝑙ℎ𝑑𝑡

∫(𝑄𝑙ℎ+𝑄𝑠ℎ)𝑑𝑡 . (26)

The 𝜂𝑅𝑅 indicates the regeneration penalization in the winter conditions. This performance index can be used to 18

size the regeneration device, and to calculate its energy consumption. 19

The number of unsatisfactory hours in the winter conditions, 𝑁𝑈𝐻, is defined as the number of hours when the 20

heating capacity of the system cannot satisfy the building heating load: 21

𝑁𝑈𝐻 = ∫ 𝑛𝑈𝐻𝑑𝑡, (27)

𝑛𝑈𝐻 = {1 , 𝑄𝐻𝑃𝐻 < 𝑄𝐵𝐻

0 , 𝑄𝐻𝑃𝐻 ≥ 𝑄𝐵𝐻 , (28)

𝑊𝐸𝐻 = ∫ max (𝑄𝐵𝐻 − 𝑄𝐻𝑃𝐻, 0)𝑑𝑡 , (29)

where 𝑄𝐵𝐻 represents the building heating load. In the unsatisfactory hours, the unsatisfied heating demands need 22

to be provided by an auxiliary electric heater, and 𝑊𝐸𝐻 is the power consumption of the electric heater. 23

By considering the energy consumption of heat pump, regeneration device, and electric heater, the energy 24

performance of the HTHP is measured by the coefficient of performance, 𝐶𝑂𝑃: 25

𝐶𝑂𝑃𝑐 =∫ 𝐶𝑝𝑤𝑀𝑐ℎ𝑤(𝑇𝑐ℎ𝑤𝑟−𝑇𝑐ℎ𝑤𝑠)𝑑𝑡

∫ 𝑊𝐻𝑃𝐶𝑑𝑡 , (30)

𝐶𝑂𝑃ℎ =∫ 𝐶𝑝𝑤𝑀ℎ𝑤(𝑇ℎ𝑤𝑠−𝑇ℎ𝑤𝑟)𝑑𝑡

∫(𝑊𝐻𝑃𝐻+𝑊𝑅𝐷+𝑊𝐸𝐻)𝑑𝑡 , (31)

𝐶𝑂𝑃𝑎 =∫ 𝐶𝑝𝑤𝑀𝑐ℎ𝑤(𝑇𝑐ℎ𝑤𝑟−𝑇𝑐ℎ𝑤𝑠)𝑑𝑡+∫ 𝐶𝑝ℎ𝑤𝑀𝑤(𝑇ℎ𝑤𝑠−𝑇ℎ𝑤𝑟)𝑑𝑡

∫ 𝑊𝐻𝑃𝐶𝑑𝑡+∫(𝑊𝐻𝑃𝐻+𝑊𝑅𝐷+𝑊𝐸𝐻)𝑑𝑡 , (32)

where the subscripts 𝑐, ℎ, 𝑎 represent cooling season, heating season, and annual, respectively. The 𝑊𝐻𝑃𝐶 and 1

𝑊𝐻𝑃𝐻 are heat pump power consumptions in cooling and heating modes, respectively. 2

3.6. Development of color map 3

To demonstrate the distributions of all the performance indices for different locations, color maps are developed 4

by combining the indices and calibrations of the color bars, as shown in Table 5. For instance, Shanghai, China is 5

selected as the specific location, whose longitude and latitude are 121.47 and 31.40, respectively. The 𝐶𝑂𝑃𝑎 of 6

Shanghai is 4.50, and its [R, G, B] matrix is between [0, 255, 255] and [255, 255, 0]. As the 𝐶𝑂𝑃𝑎 increases from 7

4.0 to 5.0, the R increases from 0 to 255, and the B decreases from 255 to 0 linearly. Therefore, we can obtain the 8

[R, G, B] matrix by solve the following equations: (R+1) / (255+1) = 𝐶𝑂𝑃𝑎- 4.0, (B+1) / (255+1) = 5.0- 𝐶𝑂𝑃𝑎. So, 9

the [R, G, B] is calculated to be [127, 255, 127]. Similarly, the [R, G, B] matrixes of all the performance indices for 10

different locations can be obtained, and the color maps are able to be developed based on the results. 11

Table 5. Calibrations of color bars 12

Color [R, G, B] 𝐶𝑂𝑃𝑐 𝜂𝑅𝑅 𝑁𝑈𝐻 𝐶𝑂𝑃ℎ 𝐶𝑂𝑃𝑎 𝜂𝑀𝐷𝐻𝑃 𝜂𝑀𝐷𝐻𝑇

[0, 0, 0] 5.0 -35% -150 2.0 2.0 0.4 0.4

[0, 0, 255] 5.5 -20% 0 2.5 3.0 0.7 0.6

[0, 255, 255] 6.0 -5% 150 3.0 4.0 1.0 0.8

[255, 255, 0] 6.5 10% 300 3.5 5.0 1.3 1.0

[255, 0, 0] 7.0 25% 450 4.0 6.0 1.6 1.2

[0, 0, 0] 7.5 40% 600 4.5 7.0 1.9 1.4

4. Results and discussion 13

According to the steps indicated in Section 3, hourly simulations of the 869 locations are carried out for a 14

whole year. Based on the results, locations which need cooling or heating supply only for a few days are excluded, 15

such as locations in Canada, England, south Australia. Seven performance indices for the remaining 762 locations 16

are calculated, and presented in color map. 17

4.1. Performance in cooling season 18

The 𝐶𝑂𝑃𝑐 of the HTHPs in cooling season vary from 5.13 to 7.40, as demonstrated in Fig. 7 to Fig. 10. Since 19

the HTHP works like a water-cooled chiller with a cooling tower in cooling season, the 𝐶𝑂𝑃𝑐 is mainly influenced 20

by the air wet-bulb temperature, which is determined the air dry-bulb temperature and relative humidity. As a result, 1

the locations with lower air dry-bulb temperature or relative humidity have higher 𝐶𝑂𝑃𝑐 , such as the ones in 2

plateaus (Colorado and Utah of the USA, Xinjiang and Gansu province of China) or with maritime climate 3

(California of the USA, Yunnan province of China, Salamanca of Spain). In general, the 𝐶𝑂𝑃𝑐 increases as the 4

latitude increase because the air dry-bulb temperature usually increases with the latitude. The average 𝐶𝑂𝑃𝑐 is 5.73 5

in Zone 3 (warm), 5.83 in Zone 4 (mixed), and 6.14 in Zone 5 (cool). 6

Fig. 7. COPc of HTHPs over the world

7

Fig. 8. COPc of HTHPs in China

1

Fig. 9. COPc of HTHPs in the USA

2

Fig. 10. COPc of HTHPs in Europe

4.2. Performance in heating season 1

The 𝜂𝑅𝑅 of the HTHPs which indicates the regeneration penalization (energy consumption of the regeneration 2

device) in the heating season, is an important index. The 𝜂𝑅𝑅 of different locations varies from -33.2% to 34.0%, 3

as presented in Fig. 11. When the 𝜂𝑅𝑅 is lager than zero, it means that the solution absorbs latent heat from the air 4

and needs additional energy for solution regeneration. Although the absorbed latent can raise the solution 5

temperature, the HTHP costs more electric energy by the regeneration device. In addition, the initial cost also 6

increases with larger regeneration capacity. When the 𝜂𝑅𝑅 is less than zero, it means that the HTHP system can 7

achieve the mass balance without addition regeneration. However, the evaporation of water reduces the temperature 8

of the solution, which can reduce the efficiency of the system. Therefore, the locations whose 𝜂𝑅𝑅 is close to zero 9

are considered to be better. These locations are marked in light green in Fig. 11, including east-central China, north-10

central of the USA. The mean relative humidity of these locations in heating season are around 70%. The locations 11

in southwest China, west coast of the USA, and west Europe, have really high 𝜂𝑅𝑅. Since the mean relative humidity 12

of these locations in heating season are between 80% and 90%. 13

Fig. 11. ηRR of HTHPs over the world

The 𝑁𝑈𝐻 is another important index, which is defined as the number of hours when the heating capacity of 1

the system cannot satisfy the building heating load. The higher 𝑁𝑈𝐻 means more energy cost by the auxiliary 2

electric heater. Due to the energy storage of the solution (absorbing latent heat in the cold and humid hours, and 3

self-regeneration in the warm and dry hours), the HTHP shows higher efficiency and capacity than the ASHP under 4

severe operating conditions[5]. However, the HTHP still has high 𝑁𝑈𝐻 when applied in the north China, north-5

central and northeast of the USA, as shown in Fig. 12. Since these regions have really low temperature in the heating 6

season. The 𝑁𝑈𝐻 of the locations with maritime climate (e.g. California of the USA, Yunnan province of China, 7

Salamanca of Spain), is close to zero, since these locations have warm heating season. 8

Fig. 12. NUH of HTHPs over the world

The 𝐶𝑂𝑃ℎ taking into account the energy consumption of the heat pump, regeneration device, and auxiliary 1

electric heater, is a comprehensive index for evaluation of HTHP’s performance in heating season. The 𝐶𝑂𝑃ℎ of 2

different locations varies from 2.24 to 4.12, as presented in Fig. 13 to Fig. 16. The 𝐶𝑂𝑃ℎ decreases as the latitude 3

increases, since the decrease of dry-bulb temperature can reduce the heat pump efficiency and increase 𝑁𝑈𝐻. The 4

average 𝐶𝑂𝑃ℎ is 3.37 in Zone 3 (warm), 2.98 in Zone 4 (mixed), and 2.73 in Zone 5 (cool). The relative humidity 5

can also have an influence on 𝐶𝑂𝑃ℎ by affecting energy cost of regeneration and heat pump efficiency as well, as 6

indicated in the analysis on 𝜂𝑅𝑅. For instance, a comparation between Chongqing (HDD18°C is 1103) and Wenzhou 7

(HDD18°C is 1106) are presented. These two locations have close latitudes and temperature, while the 𝐶𝑂𝑃ℎ of 8

Chongqing (2.83) is much lower than that of Wenzhou (3.72), as presented in Fig. 14. The mean relative humidity 9

of Chongqing in heating season (86.4%) is much higher than that of Wenzhou (70.0%). As a result, the 𝜂𝑅𝑅 of 10

Chongqing (34.1%) is much higher than that of Wenzhou (-1.3%), which means more energy consumption of 11

regeneration for Chongqing. To present the results more clearly, the 𝐶𝑂𝑃ℎ of locations in the USA are also 12

demonstrated in Fig. 15. 13

Fig. 13. COPh of HTHPs over the world

14

Fig. 14. COPh of HTHPs in China

1

Fig. 15. COPh of HTHPs in the USA

2

Fig. 16. COPh of HTHPs in Europe

4.3. Annual performance 1

Based on the results and analyses of the HTHP’s performance in both cooling and heating seasons, the annual 2

performance 𝐶𝑂𝑃𝑎 is calculated. Fig. 17 to Fig. 20 present the distributions of the 𝐶𝑂𝑃𝑎, which varies from 2.46 3

to 6.10. This index is calculated by taking into consideration of total cooling supply, 𝐶𝑂𝑃𝑐, total heating supply, 4

and 𝐶𝑂𝑃ℎ, as indicated in Eq.(32). According to the designed conditions mentioned in Section 3.3, the HTHPs in 5

cooling season have lower condensing temperature and higher evaporating temperature than the heating season. 6

Therefore, the 𝐶𝑂𝑃𝑐 is much higher than the 𝐶𝑂𝑃ℎ as presented in Sections 4.1.1 and 4.1.2. As the latitude 7

increases, the total cooling supply decreases and total heating supply increases, which means that the effect of 𝐶𝑂𝑃𝑐 8

decreases and the effect of 𝐶𝑂𝑃ℎ increases. As a result, the distribution of the 𝐶𝑂𝑃𝑎 also follows the variation of 9

latitude. The 𝐶𝑂𝑃𝑎 of Zones 3 to 5 are 4.67, 3.68, and 3.11, respectively. Specially, the locations with maritime 10

climate (e.g. California of the USA, Yunnan province of China, southwest of Europe) has higher 𝐶𝑂𝑃𝑎 because 11

these locations have cool cooling season and warm heating season. 12

Fig. 17. COPa of HTHPs over the world

1

Fig. 18. COPa of HTHPs in China

2

Fig. 19. COPa of HTHPs in the USA

1

Fig. 20. COPa of HTHPs in Europe

4.4. Matching degree of the heat pump and heating tower 1

The above five indices focus more on the operational performance, while 𝜂𝑀𝐷𝐻𝑃 and 𝜂𝑀𝐷𝐻𝑇 can make 2

contributions in the sizing and transformation process. For traditional heat pumps, such as ASHPs, the 𝜂𝑀𝐷𝐻𝑃 is 3

usually larger than 1 in their applications, which means they are designed according to the cooling mode. However, 4

the 𝜂𝑀𝐷𝐻𝑃 of the HTHPs has a much larger range when carrying out a large-scale evaluation. The results of 𝜂𝑀𝐷𝐻𝑃 5

and 𝜂𝑀𝐷𝐻𝑇 of different locations are presented in Fig. 21 and Fig. 22, respectively. The 𝜂𝑀𝐷𝐻𝑃 increases from 6

0.61 to 1.73 as the latitude increases. The locations with higher elevations (Colorado and Utah of the USA, Xinjiang 7

and Gansu province of China) or maritime climate (e.g. California of the USA, Yunnan province of China, 8

Salamanca of Spain) have lower 𝜂𝑀𝐷𝐻𝑇 than the other locations at the close latitude. When 𝜂𝑀𝐷𝐻𝑃 is larger than 9

1, it indicates that the heat pump should be sized according to the cooling mode in new HTHP system, or no add 10

additional heat pumps is required in the transformation. When 𝜂𝑀𝐷𝐻𝑃 is less than 1, the conclusions are the 11

opposite. The 𝜂𝑀𝐷𝐻𝑇 shows the similar distribution as 𝜂𝑀𝐷𝐻𝑃, and the value varies from 0.48 to 1.34, which is 12

smaller than 𝜂𝑀𝐷𝐻𝑃 in the same location. This is because the cooling capacity of the heating tower is much larger 13

than its heating capacity, as indicated in Table 4. Similarly, the heating tower should be sized to satisfy the tower 14

cooling load in new system, or no additional heating tower is required in transformation, when 𝜂𝑀𝐷𝐻𝑇 is larger 15

than 1. 16

Fig. 21. ηMDHP of HTHPs over the world

17

Fig. 22. ηMDHT of HTHPs over the world

5. Conclusion 1

Lacking performance evaluation of the HTHPs in different regions limits their applications worldwide. To 2

address this problem, this paper carries out a large-scale comprehensive performance evaluation of the HTHP in 3

869 typical locations in the warm, mixed, and cool climate zones. The performance evaluation of the HTHPs is 4

implemented by the processes of location selection, building load calculation, system sizing, simulation, and 5

evaluation. Seven performance indices are adopted, and presented for all the selected locations. The main 6

conclusions are summarized as follows: 7

(1) As the latitude increases, the 𝐶𝑂𝑃𝑐 increases from 5.13 to 7.40. The average 𝐶𝑂𝑃𝑐 is 5.73 in Zone 3 (warm), 8

5.83 in Zone 4 (mixed), and 6.14 in Zone 5 (cool). For the locations with close latitudes, these with high elevations 9

or in maritime climate show higher 𝐶𝑂𝑃𝑐. 10

(2) The 𝜂𝑅𝑅 of different locations varies from -33.2% to 34.0%, and is determined by relative humidity in heating 11

season. The 𝜂𝑅𝑅 is around zero for the locations whose mean relative humidity in winter is about 70%, including 12

east-central China and north-central of the USA. The locations whose mean relative humidity in winter is between 13

80% and 90% have really high 𝜂𝑅𝑅, including southwest China, west coast of the USA, and west Europe. 14

(3) As the latitude increases, the 𝐶𝑂𝑃ℎ of different locations decreases from 4.12 to 2.24. For the locations with 15

close latitudes, these with maritime climate or low relative humidity have higher 𝐶𝑂𝑃ℎ. 16

(4) As the latitude increases, the 𝐶𝑂𝑃𝑎 decreases from 6.10 to 2.46. The 𝐶𝑂𝑃𝑎s of Zones 3 to 5 are 4.67, 3.68, and 17

3.11, respectively. The results indicate that the HTHPs have excellent performance in Zone 3 (warm) and Zone 4 18

(mixed), and also can be applied in Zone 5 (cool). 19

(5) As the latitude increases, 𝜂𝑀𝐷𝐻𝑃 increases from 0.61 to 1.73, and 𝜂𝑀𝐷𝐻𝑇 increases from 0.48 to 1.34. The 1

distributions of these two indices can direct the design of a new HTHP system or transforming of a chiller system 2

into a HTHP system. 3

Acknowledgement 4

The research described in this paper is supported by the National Natural Science Foundation of China 5

(No.51520105009), the China National Key R & D Program (No. 2016YFC0700305), and the Scientific Research 6

Foundation of Graduate School of Southeast University (No. YBJJ1708). The research in the US is supported by 7

the National Science Foundation (No. IIS-1802017). 8

Nomenclature 9

A heat exchange area, m2 λ thermal conductivity coefficient, W m-1 K-1

Ath geometric throat area of the thermostatic

expansion, m2 ξ coefficients of Eq.(18)

CD constant mass flow coefficient ρ density, kg m-3

CDD10°C cooling degree-day base 10°C, °C ω humidity ratio，kg kg-1

COPa annual coefficient of performance, / Subscript

COPc cooling coefficient of performance, / a air

COPh heating coefficient of performance, / c condenser

Cp specific heat capacity, kJ kg-1 K-1 chws/ chwr supply / return chilled water

G mass flow flux， kg m-2 s-1 comp compressor

h enthalpy, kJ kg-1 cws / cwr supply / return cooling water

hc heat transfer coefficient of tower, W m-2 K-1 DBC designed building cooling

hd mass transfer coefficient of tower, g m-2 s-1 DBH designed building heating

HDD18°C heating degree-day base 18°C, °C e evaporator

K heat exchange coefficient, kW m-2 ℃-1 EH electric heater

L length of the packing, m HPC heat pump cooling

LMTD logarithmic mean temperature difference, ℃ HPH heat pump heating

M mass flow rate, kg s-1 HTC heating tower cooling

m mass flow rate in one element, kg s-1 HTH heating tower heating

N rotation speed, Rev. min-1 hws / hwr supply / return hot water

NUH number of unsatisfactory hours, / i inlet or inner

P pressure, Pa l liquid phase

Q heat transfer capacity, kW lh latent heat

r vaporization latent heat， kJ kg-1 m mean value of the inside and outside

R Resistance of heat transfer, m2 K W-1 MDHP matching degree of heat pump

T temperature, ℃ MDHT matching degree of heat pump

W power consumption, kW o outlet or external

X mass concentration of solution, / R refrigerant

Greek

symbols rated performance under rated speed

α coefficients of Eq.(1) RD regeneration device

αw specific area of the packing，m2 m-3 RR regeneration ratio

β coefficients of Eq.(2) s solution

γ coefficients of Eq.(17) sh sensible heat

δ thickness of the tube wall, m ss / sr supply / return solution

ηMDHP matching degree of heat pump, / UH unsatisfactory hour

ηMDHT matching degree of heat pump, / v vaper

ηRD efficiency of the regeneration system, kg kWh-1 w water

ηRR regeneration ratio, / wall wall of tube

1

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